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Air-sea exchange processes have been identified as essential for both short- and long-term atmospheric and ocean forecasts. The two phases of the fluid layer covering our planet interact across a vast range of scales that we need to explore to achieve a better understanding of the exchange processes. While satellites provide a distributed large-scale view of the sea surface situation, highly detailed measurements, e.g., from oceanographic towers, are necessarily local. The required intermediate solution (i.e., data that are both accurate and distributed) can be provided by swarms of miniature surface buoys. As size, weight, and cost are reduced, these can be deployed in large numbers to investigate specific processes that are at present only crudely parameterized in our models as a result of scarcity of good measurements. Perhaps the most crucial process is white-capping in stormy conditions, where air-sea exchanges are enhanced by one or two orders of magnitude. Other applications include wave-current interactions, wave-ice interactions, and plunging breakers in the coastal zone. Following a dedicated workshop, we summarize here the main findings and possibilities derived from the different approaches, and summarize the state of the art for a selection of miniature buoys. We list the solutions presented at the workshop, as well as other similar buoys, with their main characteristics and range of application. We describe the various possibilities of practical use and the scientific and engineering problems to be solved. Looking to the future, we also point out where the present technological improvements are leading to.

In order to perform a sensitivity analysis of Lagrangian trajectory models, Lagrangian trajectory simulations have been compared to six OpenMetBuoy-v2021 drifter trajectories in the Agulhas Current System (Jan-Mar 2023). Three different Lagrangian trajectory simulations have been assessed: (1) two offline Lagrangian tracking tools, OpenDrift and Parcels, (2) three Eulerian ocean surface current products, HYCOM, Mercator and Globcurrent, and (3) the addition of wind and/or wave forcing parameterizations. The latter has also been evaluated by strong ocean current, high wind speed and Stokes drift regimes. Firstly, using the same time stepping scheme and linear interpolation methods, the different Lagrangian simulators OpenDrift and Parcels, performed identically. Secondly, the Globcurrent product showed the highest mean skill of the three ocean current products, although it underestimated the speed for strong ocean currents due to its spatial resolution. The HYCOM and Mercator model simulations showed, respectively, 40\% and 15\% lower skill than the Globcurrent simulations. Finally, the addition of the Stokes drift and a wind drift factor (WDF), improved the Lagrangian simulation performance in skill and speed, especially in high wind (>10 m/s) and/or Stokes drift regimes (>0.15 m/s). The optimal WDF for the OpenMetBuoy-v2021 is found to be ~1.8\% and ~2.3\% for simulations including and excluding Stokes drift forcing respectively. To further improve the incorporation of Stokes drift and direct wind drag on the trajectory simulations, a more physically based solution is advised as there are still numerous wind and wave related processes that remain unresolved, like wave-current interactions and vertical shear. To statistically strengthen the conclusions from this research, incorporating additional observed drifter trajectories would be highly favourable.

The increasing number of unmanned aerial vehicles (UAVs) in urban environments requires a strategy to minimize their environmental impact, both in terms of energy efficiency and noise reduction. In order to reduce these concerns, novel strategies for developing prediction models and optimization of flight planning, for instance through deep reinforcement learning (DRL), are needed. Our goal is to develop DRL algorithms capable of enabling the autonomous navigation of UAVs in urban environments, taking into account the presence of buildings and other UAVs, optimizing the trajectories in order to reduce both energetic consumption and noise. This is achieved using fluid-flow simulations which represent the environment in which UAVs navigate and training the UAV as an agent interacting with an urban environment. In this work, we consider a domain domain represented by a two-dimensional flow field with obstacles, ideally representing buildings, extracted from a three-dimensional high-fidelity numerical simulation. The presented methodology, using PPO+LSTM cells, was validated by reproducing a simple but fundamental problem in navigation, namely the Zermelo's problem, which deals with a vessel navigating in a turbulent flow, travelling from a starting point to a target location, optimizing the trajectory. The current method shows a significant improvement with respect to both a simple PPO and a TD3 algorithm, with a success rate (SR) of the PPO+LSTM trained policy of 98.7%, and a crash rate (CR) of 0.1%, outperforming both PPO (SR = 75.6%, CR=18.6%) and TD3 (SR=77.4% and CR=14.5%). This is the first step towards DRL strategies which will guide UAVs in a three-dimensional flow field using real-time signals, making the navigation efficient in terms of flight time and avoiding damages to the vehicle.

Sea ice is a key element of the global Earth system, with a major impact on global climate and regional weather. Unfortunately, accurate sea ice modeling is challenging due to the diversity and complexity of underlying physics happening there, and a relative lack of ground truth observations. This is especially true for the Marginal Ice Zone (MIZ), which is the area where sea ice is affected by incoming ocean waves. Waves contribute to making the area dynamic, and due to the low survival time of the buoys deployed there, the MIZ is challenging to monitor. In 2022-2023, we released 79 OpenMetBuoys (OMBs) around Svalbard, both in the MIZ and the ocean immediately outside of it. OMBs are affordable enough to be deployed in large number, and gather information about drift (GPS position) and waves (1-dimensional elevation spectrum). This provides data focusing on the area around Svalbard with unprecedented spatial and temporal resolution. We expect that this will allow to perform validation and calibration of ice models and remote sensing algorithms.

Deep reinforcement learning (DRL) has found application in numerous use-cases pertaining to flow control. Multi-agent RL (MARL), a variant of DRL, has shown to be more effective than single-agent RL in controlling flows exhibiting locality and translational invariance. We present, for the first time, an implementation of MARL-based control of three-dimensional Rayleigh-B\'enard convection (RBC). Control is executed by modifying the temperature distribution along the bottom wall divided into multiple control segments, each of which acts as an independent agent. Two regimes of RBC are considered at Rayleigh numbers $\mathrm{Ra}=500$ and $750$. Evaluation of the learned control policy reveals a reduction in convection intensity by $23.5\%$ and $8.7\%$ at $\mathrm{Ra}=500$ and $750$, respectively. The MARL controller converts irregularly shaped convective patterns to regular straight rolls with lower convection that resemble flow in a relatively more stable regime. We draw comparisons with proportional control at both $\mathrm{Ra}$ and show that MARL is able to outperform the proportional controller. The learned control strategy is complex, featuring different non-linear segment-wise actuator delays and actuation magnitudes. We also perform successful evaluations on a larger domain than used for training, demonstrating that the invariant property of MARL allows direct transfer of the learnt policy., Comment: Submitted to the special issue titled 'Machine Learning for Fluid Dynamics' in the journal Flow, Turbulence and Combusion. 39 pages and 20 figures

Flow control is key to maximize energy efficiency in a wide range of applications. However, traditional flow-control methods face significant challenges in addressing non-linear systems and high-dimensional data, limiting their application in realistic energy systems. This study advances deep-reinforcement-learning (DRL) methods for flow control, particularly focusing on integrating group-invariant networks and positional encoding into DRL architectures. Our methods leverage multi-agent reinforcement learning (MARL) to exploit policy invariance in space, in combination with group-invariant networks to ensure local symmetry invariance. Additionally, a positional encoding inspired by the transformer architecture is incorporated to provide location information to the agents, mitigating action constraints from strict invariance. The proposed methods are verified using a case study of Rayleigh-B\'enard convection, where the goal is to minimize the Nusselt number Nu. The group-invariant neural networks (GI-NNs) show faster convergence compared to the base MARL, achieving better average policy performance. The GI-NNs not only cut DRL training time in half but also notably enhance learning reproducibility. Positional encoding further enhances these results, effectively reducing the minimum Nu and stabilizing convergence. Interestingly, group invariant networks specialize in improving learning speed and positional encoding specializes in improving learning quality. These results demonstrate that choosing a suitable feature-representation method according to the purpose as well as the characteristics of each control problem is essential. We believe that the results of this study will not only inspire novel DRL methods with invariant and unique representations, but also provide useful insights for industrial applications.

The coupling of weather, sea-ice, ocean, and wave forecasting systems has been a long-standing research focus to improve Arctic forecasting system and their realism and is also a priority of international initiatives such as the WMO research project PCAPS. The goal of the Svalbard Marginal Ice Zone 2024 Campaign was to observe and better understand the complex interplay between atmosphere, waves, and sea-ice in the winter Marginal Ice Zone (MIZ) in order to advance the predictive skill of coupled Arctic forecasting systems. The main objective has been to set up a network of observations with a spatial distribution that allows for a representative comparison between in situ observations and gridded model data. The observed variables include air and surface temperature, sea-ice drift, and wave energy spectra. With the support of the Norwegian Coast Guard, we participated in the research cruise with KV Svalbard from 4. April - 21.April 2024. In total 34 buoys were deployed in the Marginal Ice Zone north of the Svalbard Archipelago. The first part of the report describes the instruments and their calibration (Section 2), and the second part briefly describes the weather, sea ice, and wave conditions during the campaign., Comment: 13 pages, 11 figures, Cruise report

Technological advancements have substantially increased computational power and data availability, enabling the application of powerful machine-learning (ML) techniques across various fields. However, our ability to leverage ML methods for scientific discovery, {\it i.e.} to obtain fundamental and formalized knowledge about natural processes, is still in its infancy. In this review, we explore how the scientific community can increasingly leverage ML techniques to achieve scientific discoveries. We observe that the applicability and opportunity of ML depends strongly on the nature of the problem domain, and whether we have full ({\it e.g.}, turbulence), partial ({\it e.g.}, computational biochemistry), or no ({\it e.g.}, neuroscience) {\it a-priori} knowledge about the governing equations and physical properties of the system. Although challenges remain, principled use of ML is opening up new avenues for fundamental scientific discoveries. Throughout these diverse fields, there is a theme that ML is enabling researchers to embrace complexity in observational data that was previously intractable to classic analysis and numerical investigations.

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.

Ocean waves propagating through the Marginal Ice Zone (MIZ) and the pack ice are strongly attenuated. This attenuation is critical for protecting sea ice from energetic wave events that could otherwise lead to sea ice break-up and dislocation over large areas. Despite the importance of waves-in-ice attenuation, the exact physical mechanisms involved, and their relative importance, are still uncertain. Here we present for the first time direct in situ measurements of floe-floe interactions under the influence of waves, including collisions between adjacent floes. The collision events we report are aligned with the incoming wave direction, and phase-locked to the wave signal, which indicates that the individual collisions we detect are wave-induced. The observations demonstrate that wave attenuation by wave-induced floe-floe collisions, which have been studied in idealized laboratory and field experiments in the outer MIZ, are indeed a likely source of wave energy dissipation deep inside the MIZ as well., Comment: 18 pages, 10 figures

The control efficacy of classical periodic forcing and deep reinforcement learning (DRL) is assessed for a turbulent separation bubble (TSB) at $Re_\tau=180$ on the upstream region before separation occurs. The TSB can resemble a separation phenomenon naturally arising in wings, and a successful reduction of the TSB can have practical implications in the reduction of the aviation carbon footprint. We find that the classical zero-net-mas-flux (ZNMF) periodic control is able to reduce the TSB by 15.7%. On the other hand, the DRL-based control achieves 25.3% reduction and provides a smoother control strategy while also being ZNMF. To the best of our knowledge, the current test case is the highest Reynolds-number flow that has been successfully controlled using DRL to this date. In future work, these results will be scaled to well-resolved large-eddy simulation grids. Furthermore, we provide details of our open-source CFD-DRL framework suited for the next generation of exascale computing machines., Comment: 19 pages, 14 figures, 3 tables

Small lightweight wave buoys, SFYs, designed to operate near the coast, have been developed. The buoys are designed to record and transmit the full time series of surface acceleration at $52$ Hz. The buoy uses the cellular network to transfer data and position (up to $80$ km from the base station). This reduces costs and increases band-width. The low cost and low weight permits the buoys to be deployed easily, and in arrays in areas where satellite and wave models struggle to resolve wave and current interaction. The buoys are tested in a wave-flume, the open water and in the breaking waves of the surf. The conditions range from calm to significant wave heights exceeding $7$ m and crashing breakers with accelerations exceeding $10$ g. The high sample rate captures the impulse of breaking waves, and allows them to be studied in detail. Breaking waves are measured and quantified in the open water. We measure breaking waves in the surf and recover the trajectory of waves breaking in the field to a higher degree than previously done. The time series of surface elevation, and accurate positioning, permits the signal of adjacent buoys to be correlated in a coherent phase-resolved way. Finally, we offer an explanation and solution for the ubiquitous low-frequency noise in IMU-based buoys and discuss necessary sampling and design to measure in areas of breaking waves., Comment: 21 pages, 15 figures

Knowledge about statistics for water level variations along the coast due to storm surge is important for the utilization of the coastal zone. An open and freely available storm surge hindcast archive covering the coast of Norway and adjacent sea areas spanning the time period 1979-2022 is presented. The storm surge model is forced by wind stress and mean sea level pressure taken from the non-hydrostatic NORA3 atmospheric hindcast. A dataset consisting of observations of water level from more than 90 water level gauges along the coasts of the North Sea and the Norwegian Sea is compiled and quality controlled, and used to assess the performance of the hindcast. The observational dataset is distributed in both time and space, and when considering all the available quality controlled data, the comparison with modelled water levels yield a mean absolute error (MAE) of 9.7 cm and a root mean square error (RMSE) of 12.4 cm. Values for MAE and RMSE scaled by the standard deviation of the observed storm surge for each station are 0.42 and 0.54 standard deviations, repsectively. When considering the geographical differences in characteristics of storm surge for different countries/regions, the values of MAE and RMSE are in the range 5.7-13.9 cm and 7.6-17.8 cm respectively, and 0.33-0.46 and 0.42-0.59 standard deviations for the scaled values. The minimum and maximum values for water level in the hindcast are -2.60 m and 3.92 m. In addition, 100-year return level estimates are calculated from the hindcast, with minimum and maximum values of, respectively, -2.75 m and 3.98 m. All minimum and maximum values are found in the southern North Sea area.

An experimental study of long interfacial gravity waves was conducted in a closed wave tank containing two layers of viscous immiscible fluids. The study focuses on the development in time of the mean particle drift that occurs close to the interface where the two fluids meet. From a theoretical analysis by Weber & Christensen (Eur. J. Mech.-B/Fluids, vol. 77, 2019, pp. 162-170) it is predicted that the growing drift in this region is associated with the action of the virtual wave stress. This effect has not been explored experimentally before. Interfacial waves of different amplitudes and frequencies were produced by a D-shaped paddle. Particle tracking velocimetry (PTV) was used to track the time development of the Lagrangian mean drift. The finite geometry of the wave tank causes a mean return flow that is resolved by mass transport considerations. The measurements clearly demonstrate the importance of the virtual wave stress mechanism in generating wave drift currents near the interface.

This study reviews the design and signal processing of ship borne ultrasonic altimeter wave measurements. The system combines a downward facing ultrasonic altimeter to capture the sea surface elevation as a time series, and an inertial measurement unit to compensate for the ship's motion. The methodology is cost-effective, open source, and adaptable to various ships and platforms. The system was installed on the barque Statsraad Lehmkuhl and recorded data continuously during the 20-month One Ocean Expedition. Results from 1-month crossing of the Tropical Atlantic are presented here. The one-dimensional wave spectrum and associated wave parameters are obtained from the sea surface elevation time series. The observed significant wave height agrees well with satellite altimetry and a spectral wave model. The agreement between observations and the spectral wave model is better for the mean wave period than the peak period. We perform Doppler shift corrections to improve wave period estimates by accounting for the speed of the ship relative to the waves. This correction enhances the accuracy of the mean period, but not the peak period. We suggest that the Doppler correction could be improved by complementing the data sources with directional wave measurements from a marine X-band radar.

A drifting wave-ice buoy, which was configured by mounting the OpenMetBuoy on an ad hoc floating platform that we named Medusa, was deployed at the L\"utzow-Holm Bay (LHB) marginal ice zone in Antarctica on 4 Feb 2022 during the 63rd Japanese Antarctica research expedition. The wave-ice buoy, Medusa-766, survived the Antarctica winter as the measurement duration reached 333 days. During the winter months, it was located deep in the ice cover with the shortest distance to the ice-free Southern Ocean over 1,000 km; at this time, there was evidence of ocean wave signals at the buoy position. Using the directional wave spectra obtained from the ECMWF's reanalysis, we show that the Medusa-766 observed waves were likely generated by an extratropical cyclone in the Southern Ocean. Wave-induced ice breakup potential for such an event could extend 100s km into the ice field. When Medusa-766 was in LHB in the summer months, it did not detect sizeable wave energy despite the low sea ice concentration extent even during on-ice waves events. Characterising the considerable differences in the wave attenuation at LHB is needed to elucidate the relative contribution of ocean waves to the unstable LHB fast ice. The success of Medusa-766 demonstrates the robustness of the general design, hardware, firmware, and the high sensitivity of the sensor used. The result is promising for future LHB wave-ice interaction research.

The present study proposes an active flow control (AFC) approach based on deep reinforcement learning (DRL) to optimize the performance of multiple plasma actuators on a square cylinder. The investigation aims to modify the control inputs of the plasma actuators to reduce the drag and lift forces affecting the cylinder while maintaining a stable flow regime. The environment of the proposed model is represented by a two-dimensional direct numerical simulation (DNS) of a flow past a square cylinder. The control strategy is based on the regulation of the supplied alternating current (AC) voltage at three distinct configurations of the plasma actuators. The effectiveness of the designed strategy is first investigated for Reynolds number, $Re_{D} = 100$, and further applied for $Re_{D} = 180$. The applied active flow control strategy is able to reduce the mean drag coefficient by 97\% at $Re_{D} = 100$ and by 99\% at $Re_D=180$. Furthermore, the results from this study show that with the increase in Reynolds number, it becomes more challenging to eliminate vortex shedding with plasma actuators located only on the rear surface of the cylinder. Nevertheless, the proposed control scheme is able to completely suppress it with an optimized configuration of the plasma actuators., Comment: 30 pages, 17 figures

This paper presents for the first time successful results of active flow control with multiple independently controlled zero-net-mass-flux synthetic jets. The jets are placed on a three-dimensional cylinder along its span with the aim of reducing the drag coefficient. The method is based on a deep-reinforcement-learning framework that couples a computational-fluid-dynamics solver with an agent using the proximal-policy-optimization algorithm. We implement a multi-agent reinforcement-learning framework which offers numerous advantages: it exploits local invariants, makes the control adaptable to different geometries, facilitates transfer learning and cross-application of agents and results in significant training speedup. In this contribution we report significant drag reduction after applying the DRL-based control in three different configurations of the problem., Comment: ETMM14 2023 conference proceeding paper

In the polar regions, the interaction between waves and ice has a crucial impact on the seasonal change in the sea ice extent. However, our comprehension of this phenomenon is restricted by a lack of observations, which, in turn, results in the exclusion of associated processes from numerical models. In recent years, availability of the low-cost and accurate Inertial Motion Units has enabled the development of affordable wave research devices. Despite advancements in designing innovative open-source instruments optimized for deployment on ice floes, their customizability and survivability remain limited, especially in open waters. This study presents a novel design concept for an affordable and customizable wave buoy, aimed for wave measurements in marginal ice zones. The central focus of this wave buoy design is the application of 3D printing as rapid prototyping technology. By utilizing the high customizability offered by 3D printing, the previously developed solar-powered wave buoy was customized to install a battery pack to continue the measurements in the high latitudes for more than several months. Preliminary results from field deployments in the Pacific and Arctic Oceans demonstrate that the performance of the instruments is promising. The accuracy of frequency wave spectra measurements is found to be comparable to that of considerably more expensive instruments. Finally, the study concludes with a general evaluation of using rapid prototyping technologies for buoy designs and proposes recommendations for future designs.

This study proposes a self-learning algorithm for closed-loop cylinder wake control targeting lower drag and lower lift fluctuations with the additional challenge of sparse sensor information, taking deep reinforcement learning as the starting point. DRL performance is significantly improved by lifting the sensor signals to dynamic features (DF), which predict future flow states. The resulting dynamic feature-based DRL (DF-DRL) automatically learns a feedback control in the plant without a dynamic model. Results show that the drag coefficient of the DF-DRL model is 25% less than the vanilla model based on direct sensor feedback. More importantly, using only one surface pressure sensor, DF-DRL can reduce the drag coefficient to a state-of-the-art performance of about 8% at Re = 100 and significantly mitigate lift coefficient fluctuations. Hence, DF-DRL allows the deployment of sparse sensing of the flow without degrading the control performance. This method also shows good robustness in controlling flow under higher Reynolds numbers, which reduces the drag coefficient by 32.2% and 46.55% at Re = 500 and 1000, respectively, indicating the broad applicability of the method. Since surface pressure information is more straightforward to measure in realistic scenarios than flow velocity information, this study provides a valuable reference for experimentally designing the active flow control of a circular cylinder based on wall pressure signals, which is an essential step toward further developing intelligent control in realistic multi-input multi-output (MIMO) system.

Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for classical control-theory methods. In the present work, we apply deep reinforcement learning (DRL) for controlling RBC. We show that effective RBC control can be obtained by leveraging invariant multi-agent reinforcement learning (MARL), which takes advantage of the locality and translational invariance inherent to RBC flows inside wide channels. The MARL framework applied to RBC allows for an increase in the number of control segments without encountering the curse of dimensionality that would result from a naive increase in the DRL action-size dimension. This is made possible by the MARL ability for re-using the knowledge generated in different parts of the RBC domain. We show in a case study that MARL DRL is able to discover an advanced control strategy that destabilizes the spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing adjacent convection cells, and actively controls the resulting coalesced cell to bring it to a new stable configuration. This modified flow configuration results in reduced convective heat transfer, which is beneficial in several industrial processes. Therefore, our work both shows the potential of MARL DRL for controlling large RBC systems, as well as demonstrates the possibility for DRL to discover strategies that move the RBC configuration between different topological configurations, yielding desirable heat-transfer characteristics. These results are useful for both gaining further understanding of the intrinsic properties of RBC, as well as for developing industrial applications., Comment: 34 pages, 11 figures submitted to Physics of Fluids

Two drifting wave buoys were deployed in the central Arctic Ocean, north of the Laptev Sea, where there are historically no wave observations available. An experimental wave buoy was deployed alongside a commercial buoy. The inter-buoy comparison showed that the experimental buoy measured wave heights and periods accurately; so the buoy data were used to study the predictability of a wave-ice model in this region. The first event we focused was when both buoys observed a sudden decrease in significant wave heights $H_{m0}$. The sudden decrease was caused by the change of wind directions from along the ice edge to off-ice wind. This event was compared with the ARC MFC wave-ice model product, which underestimated the $H_{m0}$. The inaccurate model representation of an ice tongue located upwind of the buoys was found to constrain the available fetch for wave growth. The second case was when the buoys entered ice cover as new ice formed; an on-ice wave event was observed and the buoy downwind measured 1.25 m $H_{m0}$. In this instance, the ARC MFC wave-ice model product largely underestimated the downwind buoy $H_{m0}$. To investigate this event, model sea ice conditions were examined by comparing the ARC MFC sea ice forcing with the neXtSIM sea ice model product. Our analysis revealed that the thin ice thickness distribution for ice types like young and grey ice, typically less than 30 cm, were not resolved. The ARC MFC model's wave dissipation rate has a sea ice thickness dependence, and therefore, it overestimates wave dissipation in thin ice cover; sea ice forcing that can resolve the thin thickness distribution is needed to improve the predictability. This study provides an observational insight into better predictions of waves in marginal ice zones when new ice forms.

Deep reinforcement learning (DRL) has been applied to a variety of problems during the past decade, and has provided effective control strategies in high-dimensional and non-linear situations that are challenging to traditional methods. Flourishing applications now spread out into the field of fluid dynamics, and specifically of active flow control (AFC). In the community of AFC, the encouraging results obtained in two-dimensional and chaotic conditions have raised interest to study increasingly complex flows. In this review, we first provide a general overview of the reinforcement-learning (RL) and DRL frameworks, as well as their recent advances. We then focus on the application of DRL to AFC, highlighting the current limitations of the DRL algorithms in this field, and suggesting some of the potential upcoming milestones to reach, as well as open questions that are likely to attract the attention of the fluid-mechanics community.

Storm surges can give rise to extreme floods in coastal areas. The Norwegian Meteorological Institute produces 120-hour regional operational storm surge forecasts along the coast of Norway based on the Regional Ocean Modeling System (ROMS), using a model setup called Nordic4-SS. Despite advances in the development of models and computational capabilities, forecast errors remain large enough to impact response measures and issued alerts, in particular, during the strongest events. Reducing these errors will positively impact the efficiency of the warning systems while minimizing efforts and resources spent on mitigation. Here, we investigate how forecasts can be improved with residual learning, i.e., training data-driven models to predict the residuals in forecasts from Nordic4-SS. A simple error mapping technique and a more sophisticated Neural Network (NN) method are tested. Using the NN residual correction method, the Root Mean Square Error in the Oslo Fjord is reduced by 36% for lead times of one hour and 9% for 24 hours. Therefore, the residual NN method is a promising direction for correcting storm surge forecasts, especially on short timescales. Moreover, it is well adapted to being deployed operationally, as i) the correction is applied on top of the existing model and requires no changes to it, ii) all predictors used for NN inference are already available operationally, iii) prediction by the NNs is very fast, typically a few seconds per station, and iv) the NN correction can be provided to a human expert who may inspect it, compare it with the model output, and see how much correction is brought by the NN, allowing to capitalize on human expertise as a quality validation of the NN output. While no changes to the hydrodynamic model are necessary to calibrate the neural networks, they are specific to a given model and must be recalibrated when the numerical models are updated.

Cross country skiing is an interplay between the active motion of the body of the skier and the physical interaction between the surface of the skis and the snow. Friction and glide between the ski base and the snow depend on the snow temperature, ski surface chemistry and roughness, dry friction with the snow crystals and liquid meltwater film flow properties. Although a great amount of resources are being spent on understanding glide and friction, a basic physical understanding of the phenomena at play is still at large and the methodology used for assessing the gliding quality of different full scale configurations is still coarse in real world applications, which limits novel development of robust methods to control and optimize glide. Such understanding and full scale testing is particularly important for designing new ski gliders. In the present work, we develop a novel experimental setup and use it to investigate through field experiments the basic mechanical phenomena that influence glide and friction of full scale skis on snow. The field setup features a mobile, novel linear tribometer allowing investigation with whole skis in realistic cross-country conditions (speed and load). The coefficient of friction between the skis and snow is obtained from a load cell, which reports the force necessary to pull a ski sled along a flat track. Simultaneously, thermistors measure the temperature at the ski-snow interface. In addition, a GPS measures displacement and velocity. The results obtained are in good agreement with several measurements reported from similar experiments, and provide a real-world validation of results obtained in the laboratory. In addition, we release the general tribometer setup as open source material in order to provide a foundation on which other research teams as well as cross-country teams can further iterate when designing later experiments., Comment: 17 pages, 11 figures

Deep artificial neural networks (ANNs) used together with deep reinforcement learning (DRL) are receiving growing attention due to their capabilities to control complex problems. This technique has been recently used to solve problems related to flow control. In this work, an ANN trained through a DRL agent is used to perform active flow control. Two-dimensional simulations of the flow around a cylinder are conducted and an active control based on two jets located on the walls of the cylinder is considered. By gathering information from the flow surrounding the cylinder, the ANN agent is able to learn effective control strategies for the jets, leading to a significant drag reduction. In the present work, a Reynolds-number range beyond those previously considered is studied and compared with results obtained using classical flow-control methods. Significantly different nature in the control strategies is identified by the DRL as the Reynolds number Re increases. For Re <= 1000 the classical control strategy based on an opposition control relative to the wake oscillation is obtained. For Re = 2000 the new strategy consists of an energisation of the boundary layers and the separation area, which modulate the flow separation and reduce drag in a fashion similar to that of the drag crisis, through a high frequency actuation. A cross-application of agents is performed for a flow at Re = 2000, obtaining similar results in terms of drag reduction with the agents trained at Re = 1000 and 2000. The fact that two different strategies yield the same performance make us question whether this Reynolds number regime (Re = 2000) belongs to a transition towards a nature-different flow which would only admit a high-frequency actuation strategy to obtain drag reduction. This finding allows the application of ANNs trained at lower Reynolds numbers but comparable in nature, saving computational resources., Comment: 26 pages, 5 figures, submitted to MDPI

Variability in sea ice conditions, combined with strong couplings to the atmosphere and the ocean, lead to a broad range of complex sea ice dynamics. More in-situ measurements are needed to better identify the phenomena and mechanisms that govern sea ice growth, drift, and breakup. To this end, we have gathered a dataset of in-situ observations of sea ice drift and waves in ice. A total of 15 deployments were performed over a period of 5 years in both the Arctic and Antarctic, involving 72 instruments. These provide both GPS drift tracks, and measurements of waves in ice. The data can, in turn, be used for tuning sea ice drift models, investigating waves damping by sea ice, and helping calibrate other sea ice measurement techniques, such as satellite based observations.

We propose an open-source python platform for applications of Deep Reinforcement Learning (DRL) in fluid mechanics. DRL has been widely used in optimizing decision-making in nonlinear and high-dimensional problems. Here, an agent maximizes a cumulative reward with learning a feedback policy by acting in an environment. In control theory terms, the cumulative reward would correspond to the cost function, the agent to the actuator, the environment to the measured signals and the learned policy to the feedback law. Thus, DRL assumes an interactive environment or, equivalently, control plant. The setup of a numerical simulation plant with DRL is challenging and time-consuming. In this work, a novel python platform, named DRLinFluids is developed for this purpose, with DRL for flow control and optimization problems in fluid mechanics. The simulations employ OpenFOAM as popular, flexible Navier-Stokes solver in industry and academia, and Tensorforce or Tianshou as widely used versatile DRL packages. The reliability and efficiency of DRLinFluids are demonstrated for two wake stabilization benchmark problems. DRLinFluids significantly reduces the application effort of DRL in fluid mechanics and is expected to greatly accelerates academic and industrial applications.

Machine learning frameworks such as Genetic Programming (GP) and Reinforcement Learning (RL) are gaining popularity in flow control. This work presents a comparative analysis of the two, bench-marking some of their most representative algorithms against global optimization techniques such as Bayesian Optimization (BO) and Lipschitz global optimization (LIPO). First, we review the general framework of the model-free control problem, bringing together all methods as black-box optimization problems. Then, we test the control algorithms on three test cases. These are (1) the stabilization of a nonlinear dynamical system featuring frequency cross-talk, (2) the wave cancellation from a Burgers' flow and (3) the drag reduction in a cylinder wake flow. We present a comprehensive comparison to illustrate their differences in exploration versus exploitation and their balance between `model capacity' in the control law definition versus `required complexity'. We believe that such a comparison paves the way toward the hybridization of the various methods, and we offer some perspective on their future development in the literature on flow control problems., Comment: submitted to Journal of Fluid Mechanics

There is a wide consensus within the polar science, meteorology, and oceanography communities that more in-situ observations of the ocean, atmosphere, and sea ice, are required to further improve operational forecasting model skills. Traditionally, the volume of such measurements has been limited by the high cost of commercially available instruments. An increasingly attractive solution to this cost issue is to use instruments produced in-house from open source hardware, firmware, and post processing building blocks. In the present work, we release the next iteration of the open source drifter and waves monitoring instruments. The new design is both significantly less expensive, much easier to build and assemble for people without specific microelectronics and programming competence, more easily extendable and customizable, and two orders of magnitude more power efficient. Improving performance and reducing noise levels and costs compared with our previous generation of instruments is possible in large part thanks to progress from the electronics component industry. As a result, we believe that this will allow scientists in geosciences to increase by an order of magnitude the amount of in-situ data they can collect under a constant instrumentation budget. In the following, we offer 1) detailed overview of our hardware and software solution, 2) in-situ validation and benchmarking of our instrument, 3) full open source release of both hardware and software blueprints. We hope that this work, and the associated open source release, may be a milestone that will allow our scientific fields to transition towards open source, community driven instrumentation. We believe that this could have a considerable impact on many fields, by making in-situ instrumentation at least an order of magnitude less expensive and more customizable than it has been for the last 50 years., Comment: 25 pages

The motivation for this study is to investigate the abilities and limitations of a Nortek Signature1000 acoustic Doppler current profiler (ADCP) regarding fine-scale turbulence measurements. Current profilers offer the advantage of gaining more coherent measurement data than available with point acoustic measurements, and it is desirable to exploit this property in laboratory and field applications. The ADCP was tested in a towing tank, where turbulence was generated from a grid towed under controlled conditions. Grid-induced turbulence is a well-studied phenomenon and a good approximation for isotropic turbulence. Several previous experiments are available for comparison and there are developed theories within the topic. In the present experiments, an acoustic Doppler velocimeter (ADV), which is an established instrument for turbulence measurements, was applied to validate the ADCP. It was found that the mean flow measured with the ADCP was accurate within 4% of the ADV. The turbulent variance was reasonably well resolved by the ADCP when large grid bars were towed at a high speed, but largely overestimated for lower towing speed and smaller grid bars. The effective cutoff frequency and turbulent eddy size were characterized experimentally, which provides detailed guidelines for when the ADCP data can be trusted and will allow future experimentalists to decide a priori if the Nortek Signature can be used in their setup. We conclude that the ADCP is not suitable for resolving turbulent spectra in a small-scale grid-induced flow due to the intrinsic Doppler noise and the low spatial and temporal sample resolution relative to the turbulent scales.

Increased knowledge about wave attenuation processes in sea ice, and hence atmosphere-wave-ice-ocean energy transfer, is necessary to improve sea ice dynamics models used for climate modeling and offshore applications. The aim of this study is to generate such much needed data by investigating colliding ice floes dynamics in a large-scale experiment and directly measuring and quantifying the turbulent kinetic energy (TKE). The field work was carried out at Van Mijen Fjord on Svalbard, where a 3x4 m ice floe was sawed out in the fast ice. Wave motion was simulated by pulling the ice floe back and forth in an oscillatory manner in a 4x6 m pool, using two electrical winches. Ice floe motion was measured with a range meter and accelerometers, and the water turbulence was measured acoustically with an acoustic Doppler current profiler and optically with a remotely operated vehicle and bubbles as tracers. TKE frequency spectra were found to contain an inertial subrange where energy was cascading at a rate proportional to the -5/3 power law. The TKE dissipation rate was found to decrease exponentially with depth. The total TKE dissipation rate was estimated by assuming that turbulence was induced over an area corresponding to the surface of the floe. The results suggest that approximately 37% and 8% of the input power from the winches was dissipated in turbulence and absorbed in the collisions, respectively, which experimentally confirms that energy dissipation by induced turbulent water motion is an important mechanism for colliding ice floe fields.

This paper focuses on the active flow control (AFC) of the flow over a circular cylinder with synthetic jets through deep reinforcement learning (DRL) by implementing a reward function based on dynamic mode decomposition (DMD). As a main factor that affects the DRL model, the reward is determined by the information extracted from flow field by performing DMD on measurements through simulation. With the data-driven reward, the DRL model is able to learn the AFC policy through the more global information of the field, and instructs the mass flow rate of the synthetic jets. As a result of this type of AFC, the vortex street is stabilized with a reduction of approximately 8% in drag and an improvement of approximately 109% in recirculation area. Furthermore, the configuration of the flow modified by the AFC is studied with DMD on the velocity measurement of the complete flow field., Comment: arXiv admin note: text overlap with arXiv:1808.07664 by other authors

Several phenomena are known to attenuate waves in the marginal ice zone, such as wave scattering due to ice floes, viscous dissipation inside the ice and energy dissipation caused by ice floe interactions. Our aim of this study is to investigate colliding ice floes and to quantify the Turbulent Kinetic Energy (TKE) dissipation in the surrounding water through direct observations. The field work was carried out in Van Mijen Fjord on Svalbard, where an artificial 3x4 m^2 ice floe was sawed out in the 1 m thick ice. Wave motion was simulated by pulling the ice floe back and forth in an oscillatory manner with two electrical winches in a 4x6 m^2 pool. Ice floe motion was measured with a range meter, and the water turbulence was measured with acoustic velocimeters. TKE frequency spectra were found to contain an inertial subrange where energy was cascading at a rate proportional to f^(-5/3). From the spectra estimated at several vertical positions, the TKE dissipation rate was found to decrease exponentially with depth. The total TKE dissipation rate was estimated by assuming that turbulence was induced over an area spanning over the ice floe width and the pool length. The preliminary energy budget suggests that approximately 60% of the input power from the winches was dissipated in turbulence, which experimentally confirms that energy dissipation by induced turbulent water motion is an important mechanism for colliding ice floe fields., Comment: 9 pages, 5 figures, submitted to the 26th International Conference on Port and Ocean Engineering under Arctic Conditions

Due to their large mass and small aspect ratio, icebergs pose a threat to boats and offshore structures. Small icebergs and bergy bits can cause harm to platform hulls and are more difficult to discover remotely. As icebergs are dynamic mediums, the study of icebergs in relation to safe human operations requires the rigorous analysis of the ice-ocean interaction, in particular with waves and currents. In this paper, we present iceberg towing experiments and analyze iceberg stability from GPS tracks and inertial motion unit data. The towline tension as well as the boat motion relative to the iceberg was measured. Different scenarios were investigated by changing the towing strategy with regards to towing speed, direction (straight or curved trajectory) and acceleration. Large amplitude roll oscillations with period of approximately 30 s were observed immediately after the load dropped and the iceberg returned to a stable static position. In two of the cases, the iceberg flipped over partly or entirely after some towing time. From the load cell, we observed oscillations in the system with periods of approximately 6 s, which were attributed to the rope elastic properties and the iceberg response. The load oscillations increased when the towing direction was against the waves as opposed to perpendicular to the waves., Comment: 11 pages, 8 figures, submitted to the 26th International Conference on Port and Ocean Engineering under Arctic Conditions

Detailed water kinematics are important for understanding atmosphere-ice-ocean energy transfer processes in the Arctic. There are few in situ observations of 2D velocity fields in the marginal ice zone. Particle tracking velocimetry and particle image velocimetry are well known laboratory techniques for measuring 2D velocity fields, but they usually rely on fragile equipment and pollutive plastic tracers. Therefore, in order to bring these methods to the field, we have developed a new system which combines a compact open-source remotely operated vehicle as an imaging device, and air bubbles as tracing particles. The data obtained can then be analyzed using image processing techniques tuned for field measurements in the polar regions. The properties of the generated bubbles, such as the relation between terminal velocity and diameter, have been investigated under controlled conditions. The accuracy and the spread of the velocity measurements have been quantified in a wave tank and compared with theoretical solutions. Horizontal velocity components under periodic waves were measured within the order of 10% accuracy. The deviation from theoretical solutions is attributed to the bubble inertia due to the accelerated flow. We include an example from an Arctic field expedition where the system was deployed and successfully tested from an ice floe. This work is an important milestone towards performing detailed 2D flow measurements under the ice in the Arctic, which we anticipate will help perform much needed direct observations of the dynamics happening under sea ice.

Machine learning has recently become a promising technique in fluid mechanics, especially for active flow control (AFC) applications. A recent work [J. Fluid Mech. (2019), vol. 865, pp. 281-302] has demonstrated the feasibility and effectiveness of deep reinforcement learning (DRL) in performing AFC over a circular cylinder at $Re = 100$, i.e., in the laminar flow regime. As a follow-up study, we investigate the same AFC problem at an intermediate Reynolds number, i.e., $Re = 1000$, where the turbulence in the flow poses great challenges to the control. The results show that the DRL agent can still find effective control strategies, but requires much more episodes in the learning. A remarkable drag reduction of around $30\%$ is achieved, which is accompanied by elongation of the recirculation bubble and reduction of turbulent fluctuations in the cylinder wake. To our best knowledge, this study is the first successful application of DRL to AFC in weak turbulent conditions. It therefore sets a new milestone in progressing towards AFC in strong turbulent flows.

This paper focuses on the active flow control of a computational fluid dynamics simulation over a range of Reynolds numbers using deep reinforcement learning (DRL). More precisely, the proximal policy optimization (PPO) method is used to control the mass flow rate of four synthetic jets symmetrically located on the upper and lower sides of a cylinder immersed in a two-dimensional flow domain. The learning environment supports four flow configurations with Reynolds numbers 100, 200, 300 and 400, respectively. A new smoothing interpolation function is proposed to help the PPO algorithm to learn to set continuous actions, which is of great importance to effectively suppress problematic jumps in lift and allow a better convergence for the training process. It is shown that the DRL controller is able to significantly reduce the lift and drag fluctuations and to actively reduce the drag by approximately 5.7%, 21.6%, 32.7%, and 38.7%, at $Re$=100, 200, 300, and 400 respectively. More importantly, it can also effectively reduce drag for any previously unseen value of the Reynolds number between 60 and 400. This highlights the generalization ability of deep neural networks and is an important milestone to active flow control.

Increased economic activity and research interest in the Arctic raise the need for better wave forecasts in the marginal ice zone (MIZ). Mathematical and numerical models of wave propagation in sea ice would benefit from more in situ data for validation. This study presents shipborne wave measurements from the MIZ where altimeter readings are corrected for ship motion to obtain estimated single point ocean surface elevation. From the combined measurements, we obtain significant wave height and zero up-crossing period, as well as one-dimensional wave spectra. In addition, we provide spectra and integrated parameters obtained from inertial motion units (IMU) placed on ice floes inside the MIZ. The results are compared with integrated parameters from the WAM-4 spectral wave model over a period of three days in the open ocean. We also compare our measurements outside and inside the MIZ with hindcast data from the new pan-Arctic WAM-3 model and the Wave Watch III model for the European Arctic, which both model wave attenuation in sea ice. A good agreement is found with WAM-4 and WW3 in zero up-crossing period and significant wave height outside the MIZ, where deviations are less than 23%. WAM-3 is on the other hand up to 60% higher than observations. WW3 and WAM-3 are able to estimate the trends for significant wave height and zero up-crossing period inside the MIZ, although the discrepancies with respect to the observations were larger than in the open ocean. Wave damping by sea ice is investigated by looking at the spatial attenuation coefficients. Predicted attenuation coefficients are found to be 72-83% smaller for WW3 and 3-64% larger for WAM-3 compared to observations. Hence, further model tuning is necessary to better estimate wave parameters in the ice., Comment: 10 pages, 4 figures conference paper. Published at the The 25th IAHR International Symposium on Ice

The interaction between surface waves and sea ice involves many complex physical phenomena such as viscous damping, wave diffraction, and nonlinear effects. The combination of these phenomena, together with considerable variability in ice configuration, ranging from viscous grease ice slicks to large icebergs through closed drift ice and landfast ice, makes it challenging to develop robust and accurate waves in ice models. In this context, a reason for the challenges modellers are facing may lie in the mismatch between the relative scarcity of waves in ice data available for testing theories, and the wide diversity of phenomena happening at sea. This lack of experimental data may be explained, at least in part, by the high cost of waves in ice instruments. Therefore, development of open source, low-cost, high-performance instrumentation may be a critical factor in helping advance this field of research. Here, we present recent developments of a new generation of open source waves in ice instruments featuring a high accuracy Inertial Motion Unit as well as GPS, on-board processing power, solar panel, and Iridium communications. Those instruments are now being used by several groups, and their simple and modular design allows them to be customized for specific needs quickly and at reduced cost. Therefore, they may be an important factor in allowing more data to be gathered in a cost-effective way, providing much-needed data to the waves in ice community. This approach is here validated by presenting recent sea ice drift and wave activity data, and comparing these results with those obtained with commercially available buoys. In addition, our design may be used as a general platform for cost-effective development of other in-situ instruments with similar requirements of low-power data logging, on-board computational power, and satellite communications.

In recent years, Artificial Neural Networks (ANNs) and Deep Learning have become increasingly popular across a wide range of scientific and technical fields, including Fluid Mechanics. While it will take time to fully grasp the potentialities as well as the limitations of these methods, evidence is starting to accumulate that point to their potential in helping solve problems for which no theoretically optimal solution method is known. This is particularly true in Fluid Mechanics, where problems involving optimal control and optimal design are involved. Indeed, such problems are famously difficult to solve effectively with traditional methods due to the combination of non linearity, non convexity, and high dimensionality they involve. By contrast, Deep Reinforcement Learning (DRL), a method of optimization based on teaching empirical strategies to an ANN through trial and error, is well adapted to solving such problems. In this short review, we offer an insight into the current state of the art of the use of DRL within fluid mechanics, focusing on control and optimal design problems.

Increased research interest and economic activity in the Arctic raise the need for new observations of sea ice dynamics. Remote sensing as well as mathematical and numerical models of wave propagation in sea ice would benefit from more in situ data for validation. This study presents wave measurements in the marginal ice zone (MIZ) obtained from ship mounted sensors. The system combines altimeter readings from the ship bow with ship motion correction data to provide estimated single point ocean surface elevation. Significant wave height and mean wave period, as well as one-dimensional wave spectra are derived from the combined measurements. The results are compared with integrated parameters from a spectral wave model over a period of eight days in the open ocean, and with spectra and integrated parameters derived from motion detecting instruments placed on ice floes inside the MIZ. Mean absolute errors of the integrated parameters are in the range 15.0-18.9% when comparing with the spectral wave model and 1.0-9.6% when comparing with valid motion detecting instruments. The spatial wave damping coefficient is estimated by looking at the change in spectral wave amplitude found at discrete frequency values as the ship was moving along the longitudinal direction of the MIZ within time intervals where the wave field is found to be approximately constant in time. As expected from theory, high frequency waves are effectively dampened by the presence of sea ice. The observed wave attenuation rates compare favourably with a two-layer dissipation model. Our methodology can be regarded as a simple and reliable way to collect more waves-in-ice data as it can be easily added to any ship participating to ice expeditions, at little extra cost.

Instabilities arise in a number of flow configurations. One such manifestation is the development of interfacial waves in multiphase flows, such as those observed in the falling liquid film problem. Controlling the development of such instabilities is a problem of both academic and industrial interest. However, this has proven challenging in most cases due to the strong nonlinearity and high dimensionality of the underlying equations. In the present work, we successfully apply Deep Reinforcement Learning (DRL) for the control of the one-dimensional (1D) depth-integrated falling liquid film. In addition, we introduce for the first time translational invariance in the architecture of the DRL agent, and we exploit locality of the control problem to define a dense reward function. This allows to both speed up learning considerably, and to easily control an arbitrary large number of jets and overcome the curse of dimensionality on the control output size that would take place using a naive approach. This illustrates the importance of the architecture of the agent for successful DRL control, and we believe this will be an important element in the effective application of DRL to large two-dimensional (2D) or three-dimensional (3D) systems featuring translational, axisymmetric or other invariants.

Deep Reinforcement Learning (DRL) has recently spread into a range of domains within physics and engineering, with multiple remarkable achievements. Still, much remains to be explored before the capabilities of these methods are well understood. In this paper, we present the first application of DRL to direct shape optimization. We show that, given adequate reward, an artificial neural network trained through DRL is able to generate optimal shapes on its own, without any prior knowledge and in a constrained time. While we choose here to apply this methodology to aerodynamics, the optimization process itself is agnostic to details of the use case, and thus our work paves the way to new generic shape optimization strategies both in fluid mechanics, and more generally in any domain where a relevant reward function can be defined.

Deep reinforcement learning (DRL) has recently been adopted in a wide range of physics and engineering domains for its ability to solve decision-making problems that were previously out of reach due to a combination of non-linearity and high dimensionality. In the last few years, it has spread in the field of computational mechanics, and particularly in fluid dynamics, with recent applications in flow control and shape optimization. In this work, we conduct a detailed review of existing DRL applications to fluid mechanics problems. In addition, we present recent results that further illustrate the potential of DRL in Fluid Mechanics. The coupling methods used in each case are covered, detailing their advantages and limitations. Our review also focuses on the comparison with classical methods for optimal control and optimization. Finally, several test cases are described that illustrate recent progress made in this field. The goal of this publication is to provide an understanding of DRL capabilities along with state-of-the-art applications in fluid dynamics to researchers wishing to address new problems with these methods.

The results of field work on drift ice during wave propagation are analyzed and presented. The field work was performed in the Barents Sea, and the main focus of the paper is on wave processes in the MIZ. A model of wave damping in broken ice is formulated and applied to interpret the field work results. It is confirmed that waves of higher frequencies are subjected to stronger damping when they propagate below the ice. This reduces the frequency of most energetic wave with increasing distance from the ice edge. Difference of wave spectra measured in two relatively close locations within the MIZ is discussed. The complicated geometry and dynamics of the MIZ in the North-West Barents Sea allow waves from the Atlantic Ocean and south regions of the Barents Sea to penetrate into different locations of the MIZ.